the maximum heat attained within the brakes occurs up to 30 minutes after the aircraft has stopped. That is one reason why a brake fire warning can occur well into the climb after take off
And one of the reasons the FT community likes to dangle the wheels for a while after takeoff to cool the units off following any significant braking effort on test. Indeed, after RTO work, the usual procedure is to turn around and takeoff immediately solely for the purpose of flying around for 5-10 minutes with the wheels down.
I can recall at least one aircraft lost after a overheated tyre burst some time after takeoff ... not a hazard to treat lightly.